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Optimizing Expected Time Utility in Cyber-Physical Systems Schedulers
Terry Tidwell, Robert Glaubius, Christopher Gill, William Smart Washington University in St. Louis 11/19/2018 RTSS 2010
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Cyber-Physical Systems
sensor actuator CAN controller Interaction w/ real-world imposes (potential complex) timing constraints Correct execution requires respecting those timing constraints Example: controllers, sensors and actuators on CAN Two trends… jamming more stuff together with less resources Solution: scheduling Current solution… overprovisioning for worst case -expensive -potentially incorrect for some systems Based on A. Anta and P. Tabuada “On the benefits of relaxing the periodicity assumption for networked control systems over CAN”, 2010. 11/19/2018 RTSS 2010
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Cyber-Physical Systems
Problem: Current real-time scheduling abstractions are insufficient sensor actuator CAN controller Interaction w/ real-world imposes (potential complex) timing constraints Correct execution requires respecting those timing constraints Example: controllers, sensors and actuators on CAN Two trends… jamming more stuff together with less resources Solution: scheduling Current solution… overprovisioning for worst case -expensive -softer real-time systems Based on A. Anta and P. Tabuada “On the benefits of relaxing the periodicity assumption for networked control systems over CAN”, 2010. 11/19/2018 RTSS 2010
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Periodic Real-Time Task
Periodic Tasks [Lui&Layland73] Series of jobs Release time, deadlines, worst case execution time Basic scheduling goal: minimizing deadline miss rate Assuming that the problem is to make sure that work finishes early enough p 2p 3p Time 11/19/2018 RTSS 2010
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Periodic Real-Time Task
Periodic Tasks [Lui&Layland73] Series of jobs Release time, deadlines, worst case execution time Basic scheduling goal: minimizing deadline miss rate Problem: Deadline and worst case execution time only bounds behavior Two problems: one minor, one major -wcet -deadline is not always applicable p 2p 3p Time 11/19/2018 RTSS 2010
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Distributed Control Task
Designed to execute at a specific frequency Inter-job jitter can cause control instabilities Execution times may be stochastic sensor actuator CAN controller Early may be just as bad as late -stale sensor data -early actuation Exact execution completion matters -wcet insuffecient -need to deal w/ entire distribution p 2p 3p Time 11/19/2018 RTSS 2010
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Time Utility Functions
Define utility gained from completing a job as a function of time Describe richer set of timing constraints Basic scheduling problem: maximize utility accrual Utility Time Utility Deadline = urgency only Based on Figure 1 in Ravindran, et. al. “On Recent Advances in Time/Utility Function Real-Time Scheduling and Resource Management”, 2005. Time 11/19/2018 RTSS 2010
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Utility Accrual Scheduling
Utility accrual scheduling problem Stochastic execution duration Non-preemptable jobs Equivalent Markov Decision Process formulation Solutions to which is a value-optimal scheduling policy Offline policy generation Utility Time Utility Based on Figure 1 in Ravindran, et. al. “On Recent Advances in Time/Utility Function Real-Time Scheduling and Resource Management”, 2005. Time 11/19/2018 RTSS 2010
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Task Set Examples Time time-utility function period boundary
termination time period boundary period boundary termination time Time 11/19/2018 RTSS 2010
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System State Evolution
State = <RunQ, System Time> 8 RunQ RunQ +Utility 11/19/2018 RTSS 2010
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System State Evolution
Non work conserving scheduling options (No utility gained) 8 9 RunQ RunQ 11/19/2018 RTSS 2010
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System State Evolution
Each scheduling action may stochastically transition to one of many states. 8 11 RunQ RunQ +Utility 11/19/2018 RTSS 2010
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System State Evolution
9 RunQ 10 RunQ 11 8 RunQ RunQ 11/19/2018 RTSS 2010
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State Space Example time time time 2 tasks with unit duration
Termination time and periods for task 1 = 2 for task 2 = 4 Hyperperiod = 4 Termination time and hyperperiod guarantee a finite number of states idle action action 1 action 2 time time time 11/19/2018 RTSS 2010
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A scheduling policy is a function, π, mapping states to actions
Scheduling Policies A scheduling policy is a function, π, mapping states to actions x0 x1 x2 x3 + V(π) = r0 + r1 + r2 11/19/2018 RTSS 2010
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Scheduling Policies x0 x1 x2 x3 + V(π) = r0 t0 – t1 + r1 t1 – t2 + r2
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V(π) is the value of the policy
Scheduling Policies 0 ≤ γ ≤ 1 x0 x1 x2 x3 + V(π) = γ0 r0 t0 – t1 + γ1 r1 t1 – t2 + γ2 r2 t2 – t3 V(π) is the value of the policy 11/19/2018 RTSS 2010
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V(π) is the value of the policy
Scheduling Policies 0 ≤ γ ≤ 1 Existing techniques can generate scheduling policies that optimize value x0 x1 x2 x3 + V(π) = γ0 r0 t0 – t1 + γ1 r1 t1 – t2 + γ2 r2 t2 – t3 V(π) is the value of the policy 11/19/2018 RTSS 2010
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Simulation Experiments
(downward step) Different number of tasks Different shaped time utility functions Parameterized curves Stochastic execution Compared to greedy Generic Benefit Scheduler [P. Li ’04] (linear drop) (target sensitive) 11/19/2018 RTSS 2010
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Results Effect of Time Utility Function Shape
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Results Effect of Number of Tasks
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Conclusions Real-time scheduling abstractions like deadlines and worst case execution time may not cover all cyber-physical systems Scheduling policies needed for systems with time utility functions and stochastic execution Markov Decision Process formulation can give value-optimal utility accrual scheduling policies 11/19/2018 RTSS 2010
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